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Scilab help >> Scilab > Scilab keywords > power

# power

(^,.^) power operation

```t=A^b
t=A**b
t=A.^b```

### Arguments

A,t

scalar, polynomial or rational matrix.

b

a scalar, a vector or a scalar matrix.

### Description

• If `A` is a square matrix and `b` is a scalar then `A^b` is the matrix `A` to the power `b`.

• If `b` is a scalar and `A` a matrix then `A.^b` is the matrix formed by the element of `A` to the power `b` (element-wise power). If `A` is a vector and `b` is a scalar then `A^b` and `A.^b` performs the same operation (i.e. element-wise power).

• If `A` is a scalar and `b` is a matrix (or vector) `A^b` and `A.^b` are the matrices (or vectors) formed by `a^(b(i,j))`.

• If `A` and `b` are vectors (matrices) of the same size `A.^b` is the `A(i)^b(i)` vector (`A(i,j)^b(i,j)` matrix).

Notes:

- For square matrices `A^p` is computed through successive matrices multiplications if `p` is a positive integer, and by diagonalization if not.

- `**` and `^` operators are synonyms.

### Examples

```A=[1 2;3 4];
A^2.5,
A.^2.5
(1:10)^2
(1:10).^2

s=poly(0,'s')
s^(1:10)```